# Skilling success rate

The skilling success function is used to determine whether or not a skilling action rewards the player, typically with an item and experience. The formula approximates a linear interpolation. As the player's level in a skill increases, the rate of success generally increases as well.

Each action that uses the skilling success function takes two parameters, a "low" value and a "high" value, to use. These low and high values are unique to that action and do not change regardless of the player's level, but they can change if the player meets certain conditions, such as having a Thieving cape equipped. For a given level L, the chance of success can be determined from the skilling success formula:

${\displaystyle P(L)={\frac {1+(\lfloor {\frac {low\times (99-L)}{98}}\rfloor +\lfloor {\frac {high\times (L-1)}{98}}\rfloor )}{256}}}$

Due to the floor functions that result from the engine's integer division, in certain cases the chance of success may actually decrease as the player's level increases. This can be seen in the skilling success chart for fishing raw monkfish below:

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Some activities like barbarian fishing and Herbiboar follow a cascading format, where multiple skilling success formulas are used to determine what the player receives. Generally, the highest reward the player can receive is rolled first, and if the player fails the roll, they go on to the next roll until either succeeding a roll or failing all the rolls.

For example, a player using the barbarian rod with 85 Fishing as well as the other requirements to catch a leaping sturgeon first rolls against the skilling success formula for leaping sturgeon. Since leaping sturgeon have a low value of 8 and a high value of 64, the chance of getting a leaping sturgeon is

${\displaystyle P_{sturgeon}(85)={\frac {1+(\lfloor {\frac {8\times (99-85)}{98}}\rfloor +\lfloor {\frac {64\times (85-1)}{98}}\rfloor )}{256}}={\frac {1+(\lfloor {\frac {112}{98}}\rfloor +\lfloor {\frac {5376}{98}}\rfloor )}{256}}={\frac {1+1+54}{256}}=0.21875}$

If the player fails to get a leaping sturgeon, a leaping salmon is rolled for. Since leaping salmon have a low value of 16 and a high value of 96, the chance of getting a leaping salmon given that the player failed the leaping sturgeon roll is

${\displaystyle P_{salmon}(85)={\frac {1+(\lfloor {\frac {16\times (99-85)}{98}}\rfloor +\lfloor {\frac {96\times (85-1)}{98}}\rfloor )}{256}}={\frac {1+(\lfloor {\frac {224}{98}}\rfloor +\lfloor {\frac {8064}{98}}\rfloor )}{256}}={\frac {1+2+82}{256}}\approx 0.33203}$

So the chance of failing to catch a sturgeon and instead catching a leaping salmon at level 85 is

${\displaystyle (1-P_{sturgeon}(85))*P_{salmon}(85)\approx (1-0.21875)*0.33203\approx 0.2594}$

Similarly, the chance that a player fails to catch both a leaping sturgeon and leaping salmon, but catches a leaping trout, which has a low value of 32 and a high value of 192, is

${\displaystyle (1-P_{sturgeon}(85))*(1-P_{salmon}(85))*P_{trout}(85)\approx 0.3445}$

If the all three rolls are failed, the player receives nothing.

## Boosts over 99

The skilling success function's input is clamped to a maximum value of 99. When boosting over 99 using invisible boosts like the celestial ring, a similar formula is used to calculate success chance. In the case of visible boosts, the boost over 99 is disregarded entirely. In situations where the skilling success formula is not used, like aerial fishing, this is not necessarily the case.